Simple Harmonic Motion Flashcards

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1
Q

How do you calculate the total energy of an SHM oscillator from its amplitude?

A

E = ½ k A²

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2
Q

At what displacement is the potential energy of an SHM oscillator at a maximum?

A

At maximum displacement, (x=±A)

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3
Q

How does the total energy in an SHM oscillator vary with time?

A

It remains constant.

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4
Q

What is the kinetic energy of an SHM oscillator at maximum displacement?

A

Zero.

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5
Q

What measures can be taken to improve the accuracy when measuring the time period of SHM?

A

Time over multiple (at least 10) oscillations and calculate the average of several repeats.

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6
Q

What is a fiducial marker?

A

A pin or pointer placed at the equilibrium position of an oscillation.

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7
Q

What is an isochronous oscillator?

A

An oscillator with a period that is independent of amplitude.

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8
Q

What is the acceleration of an object undergoing SHM when its displacement is zero?

A

Zero.

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9
Q

What are the conditions required for SHM?

A

The acceleration of an object is proportional to its displacement from equilibrium, and always in the opposite direction.

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10
Q

How do you calculate the angular frequency of an oscillation?

A

angular frequency = 2 * pi * frequency

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11
Q

How many radians are there in one complete oscillation?

A

2 * pi

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12
Q

What is the equilibrium position in an oscillation?

A

The point at which an object experiences no resultant force and thus no acceleration. (The ‘rest’ position of an object).

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13
Q

What is a free oscillation?

A

An oscillation in which no external driving force is present.

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14
Q

What causes damping of an oscillation?

A

An external force opposing motion.

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15
Q

What effect does damping of an oscillation have in terms of energy?

A

It transfers the KE of the oscillation to other forms, usually thermal energy.

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16
Q

What is light damping of an oscillation?

A

A small damping force causing the amplitude of the oscillations to decrease slowly.

17
Q

What is heavy damping of an oscillation?

A

A damping force that results in a rapid decrease in the amplitude of oscillations.

18
Q

What is very heavy or over-damping of an oscillation?

A

A large damping force that prevents any oscillations of the system when it is displaced from equilibrium.

19
Q

What is the natural frequency of an oscillator?

A

The frequency at which oscillation will occur in a system with no external driving forces (i.e. free oscillations).

20
Q

What is a forced oscillation?

A

An oscillation in which a (periodic) external driving force is present.

21
Q

What is a driving frequency in oscillations?

A

The frequency of the external driving force in a forced oscillation.

22
Q

What is resonance?

A

When the driving frequency of a forced oscillation is close to the natural frequency of the system resulting in large amplitude oscillations.

23
Q

What is likely to occur when a mechanical system with little or no damping resonates?

A

The amplitude of the oscillations will increase until the object breaks.

24
Q

What occurs in terms of energy during resonance?

A

There is the greatest possible transfer of energy from the driver to the forced oscillation.

25
Q

What effect does increasing damping have on resonance?

A

It reduces the maximum amplitude and it reduces the frequency of maximum amplitude.

26
Q

What is the equation for the Time period of a pendulum?

A

T = 2 * pi * sqrt(l/g)

27
Q

What is the equation for the time period of a mass on a spring?

A

T = 2 * pi * sqrt (m/k)

28
Q

How does the displacement vary with time for an oscillator released from maximum amplitude at t = 0?

A

x = A cos (omega*t)

29
Q

How does velocity vary as a function of displacement in SHM?

A

v = +/- omega * sqrt ( A^2 - x^2)

30
Q

What 3 changes happens to the resonance graph for increasing levels of damping?

A
  1. Amplitude decreases
  2. Amplitude curve gets broader
  3. Resonance shifts to lower frequency (left)